%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:16:52 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 25 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t1) ).
cnf(c_54,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(b2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ between(VAR_1,VAR_0,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b2) ).
cnf(c_56,plain,
( A = B
| ~ between(B,A,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b2]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_57,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(w_between_u_and_v,axiom,
between(u,w,v),
file('theBenchmark.p',w_between_u_and_v) ).
cnf(c_58,plain,
between(u,w,v),
inference(clausify,[status(thm)],[w_between_u_and_v]) ).
fof(prove_v_is_w,axiom,
v != w,
file('theBenchmark.p',prove_v_is_w) ).
cnf(c_59,plain,
v != w,
inference(clausify,[status(thm)],[prove_v_is_w]) ).
cnf(c_60,plain,
w != v,
inference(copy,[status(thm)],[c_59]) ).
cnf(c_174,plain,
between(w,v,u),
inference(resolve,[status(thm)],[c_57,c_54]) ).
cnf(c_196,plain,
between(v,w,u),
inference(resolve,[status(thm)],[c_58,c_54]) ).
cnf(c_277,plain,
( v = w
| ~ between(v,w,u) ),
inference(resolve,[status(thm)],[c_174,c_56]) ).
cnf(c_278,plain,
( w = v
| ~ between(v,w,u) ),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_279,plain,
w = v,
inference(resolve,[status(thm)],[c_196,c_278]) ).
cnf(c_276,plain,
$false,
inference(resolve,[status(thm)],[c_60,c_279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 12:37:50 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3274277 was started by sandbox on n002,
% 0.14/0.36 % Fri Sep 25 12:37:50 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.14/0.44 % Length of proof is 9.
% 0.14/0.44 % Level of proof is 2.
% 0.14/0.44 % Maximum clause weight is 13.000.
% 0.14/0.44 % Given clauses 61.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------